Project Zero II: Crimson Butterfly. You folks in the US will know it as Fatal Frame II. I played it on the PS2 but apparently it's out for Wii now. That game is just eerie all the way through, and has some very nerve-jangling moments. A lot of it is more psychological than an outright gore-fest.
Another one is Forbidden Siren (also PS2). That game is very creepy and also very "run away screaming", since most of the time that's all you can do. There's a sort of sequel available on PSN, called Siren: Blood Curse. I haven't played beyond the first episode of that but it's more of the same.
Finally, the first Dead Space game. That one is really awesome for making you almost jump out of your skin. The feeling of claustrophobia is almost overwhelming. The series has been watered down a little since then, but the original one does a really good job with the horror. Great story, too.